I’m confused, shouldn’t it be 0?
In: Mathematics
Let’s use 2^(n) as example. We know that 2^(1)=2, 2^(2)=4, 2^(3)=8, etc… In general, when you add 1 to the exponent, you multiply the overall number by 2. Now work backwards: if you subtract 1 from the exponent, you’d be dividing the number by 2. So from that logic, 2^(2) = 2^(3)/2 = 8/2 = 4. Continuing, we get 2^(1) = 4/2 = 2. And doing it again, 2^(0) = 2/2 = 1. You can do this with any number (except 0) to show that x^(0) = 1.
This also explains how negative exponents work. By continuing subtracting the exponent, we get 2^(-1)=1/2, 2^(-2)=1/4, and in general, 2^(-n)=1/2^(n).
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